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Fig. 1.

Fig. 1. Refer to the following caption and surrounding text.

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Top: Waterfall plot of stacked Lomb-Scargle periodograms. The right Y-axis indicates the middle MJD of each five-day slice, with the color gradient representing temporal progression. It illustrates the secular evolution of the spin frequency over the ∼56-day TESS observation baseline. Flanking the central period, two periods are observed that we identify as the beat periods between the orbital and spin periods (see Section 3.1). Middle: Evolution of the spin period as a function of time (MJD). The black points denote measurements from individual sliding windows, with 1σ uncertainties derived from 200-iteration Monte Carlo simulations integrated with an AR(p) red noise model. The red line represents a WLS linear fit, yielding a secular spin-down rate of = 1.91 × 10−8±7.01 × 10−10 s/s, which represents a 20.9σ significance level over the constant hypothesis. The residuals of the linear period fit show no systematic trends or higher-order derivatives. Bottom: Pulse profile (50 bins) constructed via quadratic phase folding using the derived ephemeris ( ϕ ( t ) = f 0 Δ t + 1 2 f ˙ Δ t 2 Mathematical equation: $ \phi(t) = f_0 \Delta t + \frac{1}{2} \dot{f} \Delta t^2 $). The phase-folded profile is dominated by a broad, quasi-sinusoidal modulation. The successful recovery of this complex structure across the full TESS baseline confirms high phase coherence (Q = 1/|| ≈ 5.2 × 107) and validates the quadratic timing correction ( = 1.91 × 10−8 s/s).

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